2012 Toyota Tacoma 4.0l Battery Light on

So I'm working on a 2012 Tacoma 4.0l. The battery light will come on at times intermittently. When its on, the alternator is charging properly at around 13.5v. Can someone explain to me how this L circuit works so I can better understand? Am I correct to say that the regulator within the alternator is what grounds the L circuit which then turns the battery light on? What is have seen is that when the battery light is on,  the L circuit is grounded and the other 2 wires are at B+. When the battery light is off, the L circuit reads around 12v, the other 2 around 13.5v, should the L circuit match charging system voltage? If I unplug the alternator, the battery light goes away and the L circuit then reads 12v. This indicates a faulty alternator regulator correct? It is grounding the L circuit when it shouldn't be. Also, how does that body module tied into the L circuit come into play? Thanks for any advice.

UPDATE: ALTERNATOR FIXED THE PROBLEM

Can someone explain to me how this L circuit works so I can better understand? Am I correct to say that the regulator within the alternator is what grounds the L circuit which then turns the battery light on?

100% correct about the regulator in the alternator grounding the L circuit. If you felt like proving this to yourself, you could turn the key on, disconnect the alternator and ground the grey wire with a test light. You should be able to make the battery light come and go as you like.

What is have seen is that when the battery light is on,  the L circuit is grounded and the other 2 wires are at B+. When the battery light is off, the L circuit reads around 12v, the other 2 around 13.5v, should the L circuit match charging system voltage?

You'd think! But I've noticed that it's normal for most light control circuits to sit below system voltage. I'm no engineer, but I'm guessing it has to do with the construction/design of the light circuit in the combination meter. I wouldn't sweat your voltage readings at this point.

If I unplug the alternator, the battery light goes away and the L circuit then reads 12v. This indicates a faulty alternator regulator correct? It is grounding the L circuit when it shouldn't be.

Just to be clear - Did you unplug the alternator *while* the battery light was coming on? If so, you're done, faulty alternator.

Also, how does that body module tied into the L circuit come into play?

That's a very good question! I dug through service info for a bit and couldn't find anything that mentions this branch of the L circuit.

'Multiplexing' comes up a lot when reading about the Body ECU. So, I'm gonna figure that the L terminal is an input to the Body ECU, and not a way for the Body ECU to control the battery light. Why does the Body ECU need a direct line from the alternator? No clue.